Kanellopoulos

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These are answers submitted by Kanellopoulos

You are right that the problem must be mailny in the numerical sceme..Do you have in mind any "trick" that will allow me too see any moments later?? (like "continuation"  for the ODEs)

Thanks!

The most probably, there exist a singularity,but i cannot imagine that goes to infinity so fast...For t=0.188 is stil a solid soliton-like wave, of course with signs of instability..and then for t=0.189 the error message...for my point of view i should witness the colapse of the wave...

Thanx a lot!

Thanx a lot,

i didn't do the Optimimization part,without it Maple 12 returns it unevaluated.

For derivative i used:

>fsolve(diff(g(x),x),x=1);

 0.9805089961

Thanx a lot!

I see, there isn't a fixed method for PDEs.. you have to built the theory...

About numerical methods, i have a Hyperbolic type PDE first order and i used ForwardTime1space, and for a Parabolic type second order,i used BackwardEuler

Are any other suggestions??

Honestly i dont know if maple  has fixed commands  for  making  bifurcations...If i were you i would try to find the stable points for many different values of e (with all the others fixed) and then make a pointplot...As in Logistic map...Also your system seems a bit strange to me, the fisrt equation is only dependent of x(t) so you can solve the first by its own, and then you will have only one ode....I cant think anything else...

Good luck!

Giorgos

 

 

Hi! First of all the second equation is incomplete, a parenthesis missing...

I use DE(plot) for such systems but you need initial or boundary conditions..I tried something like this:

 

>with(DEtools):

>a:=7: b:=1.4: c:=0.2: d:=0.1: e:=2.1; f:=0.5:g:=2.8:


> DEplot([D(x)(t)=a*b*((x(t)^2+c^2)/(x(t)^2+1))-d*x(t)
 ,D(y)(t)=a*e*((y(t)^3+f^3)/(x(t)^3+1))*(g*x(t)+1)-y(t)],
 [x(t),y(t)],t=-5..5,[[x(0)=0,y(0)=0]],stepsize=.05);
 

Giorgos

thanx friend it worked with a bit change: (here my solution if you are interested)

>for k from 1 to 100 by 5 do

A[k]:=ColumnGraph(points[k],color=blue,axes=BOXED,thickness=2,print(t=k),view=[0..26,0..0.1]);

od:

 

>for k from 1 to 100 by 5 do
n:=k:
plotsetup(jpeg,plotoutput=cat(convert(k,string),`.jpg`));
A[n];
od;

 

 Thanx again!!

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